ANALYTICAL TREATMENT OF RADIATION AND CONDUCTION LOSSES IN THERMAL INDUCTION PLASMAS.
Research rept. Jun 68-Jan 69,
AEROSPACE CORP EL SEGUNDO CALIF LAB OPERATIONS
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Approximate solutions have been obtained of the Elenbaas-Heller equation for a two-zone model of thermal induction plasmas. In this model, most of the heat production takes place in an external zone where it is balanced by heat conduction, radiation losses being negligible in this region. Most of the heat so generated is conducted to the walls, but a small fraction of it is conducted inward and forms the principal heat source for the second, internal, zone. Radiation is the dominant loss mechanism in this inner region. Under these conditions, the distribution of the heat conduction potential assumes a parabolic shape for the inner zone, whereas it is described by Bessel functions in the external zone. A coordinate transformation in this zone accounts for the nonuniformity of the induced electric field and explicitly shows the effect of skin depth upon the profile shape. Matching of the zonewise solutions yields temperature distributions that are continuous to the first derivative and display the characteristic minimum at the axis known from experimental work. Generalized charts are presented by which a particular profile can be calculated from the gas transport properties and the time rate of change of primary magnetic flux. Author
- Plasma Physics and Magnetohydrodynamics